For example, a diesel particulate filter (referred to as “DPF” hereinafter) is known as a filter to collect particulate matter contained in an exhaust gas discharged from a diesel engine. Because the DPF has a limitation on an amount of particulate matter to be collected, it is necessary to periodically carry out regeneration, i.e., burning the accumulated particulate matter for removal of the accumulated particle matter. The regeneration of the DPF is performed by feeding an unburnt fuel to an oxidation catalyst provided upstream of the DPF by fuel injection into the exhaust pipe or by post injection. With such fuel injection, heat is generated upon oxidation, and the heat elevates the exhaust gas temperature to a PM combustion temperature.